Konsistensi Aksioma-Aksioma Terhadap Istilah-Istilah Takterdefinisi Geometri Hiperbolik Pada Model Piringan Poincare

Putra Pratama, Febriyana Konsistensi Aksioma-Aksioma Terhadap Istilah-Istilah Takterdefinisi Geometri Hiperbolik Pada Model Piringan Poincare. [Artikel Dosen]

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Abstract

This research aims to know the interpretation the undefined terms on Hyperbolic geometry and it’s consistence with
respect to own axioms of Poincare disk model. This research is a literature study that discusses about Hyperbolic
geometry. This study refers to books of Foundation of Geometry second edition by Gerard A. Venema (2012),
Euclidean and Non Euclidean Geometry (Development and History) by Greenberg (1994), Geometry : Euclid and
Beyond by Hartshorne (2000) and Euclidean Geometry: A First Course by M. Solomonovich (2010). The steps taken
in the study are: (1) reviewing the various references on the topic of Hyperbolic geometry. (2) representing the
definitions and theorems on which the Hyperbolic geometry is based. (3) prepare all materials that have been
collected in coherence to facilitate the reader in understanding it. This research succeeded in interpret the
undefined terms of Hyperbolic geometry on Poincare disk model. The point is coincide point in the Euclid on circle
. Then the point onl γ is not an Euclid point. That point interprets the point on infinity. Lines are categoried in two
types. The first type is any open diameters of . The second type is any open arcs of circle. Half-plane in Poincare
disk model is formed by Poincare line which divides Poincare field into two parts. The angle in this model is
interpreted the same as the angle in Euclid geometry. The distance is interpreted in Poincare disk model defined by
the cross-ratio as follows. The definition of distance from to is , where is
cross-ratio defined by ̅̅̅̅ ̅̅̅̅ ̅̅̅̅ ̅̅̅̅ . Finally the study also is able to show that axioms of
Hyperbolic geometry on the Poincare disk model consistent with respect to associated undefined terms

Item Type:	Artikel Dosen
Subjects:	Q Science > QA Mathematics
Divisi / Prodi:	Faculty of Applied Science and Technology (Fakultas Sains Dan Teknologi Terapan) > S1-Mathematics (S1-Matematika)
Depositing User:	Dr. Julan Hernadi
Date Deposited:	04 Jan 2023 02:52
Last Modified:	04 Jan 2023 02:52
URI:	http://eprints.uad.ac.id/id/eprint/38403

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